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IMLOG (ComplexNumber,Base)

  • is any complex number of the form x+iy.
  • is the base value of the Log.
    • IMLOG(),returns the logarithm of a complex number to the given base.


  • This function shows the log value of a complex number.
  • In , is any complex number.
  • is the base value of a Log values.
  • A complex logarithm function is an "inverse" of the complex exponential function.
  • It is same as the real natural logarithm ln x is the inverse of the real exponential function.
  • Thus, a logarithm of a complex number z is a complex number w such that .
  • The notation for such a is or .
  • If with which is in Polar form, then is one logarithm of z.
  • Adding integer multiples of 2πi gives all the others.
  • The complex exponential function is not injective, because for any w, since adding iθ to w has the effect of rotating counterclockwise θ radians.
  • So the points


  1. IMLOG("2+3i",2) = 1.850219859070546+ⅈ1.417871630745722
  2. IMLOG("9-5i",3) = 2.122422597222964-ⅈ0.4615809504617068
  3. IMLOG("9-5i",6) = 1.3013574573492332-ⅈ0.2830170640096076
  4. IMLOG("54",5) =2.4784951415313494+ⅈ0
  5. IMLOG("-19i",9) = 1.3400719296231876-ⅈ0.7149002168450317

Related Videos

Complex Logarithm

See Also